U.S. patent application number 11/230159 was filed with the patent office on 2007-03-22 for method and apparatus for modifying an electromagnetic radiation beam.
Invention is credited to Shih-Yuan Wang.
Application Number | 20070065068 11/230159 |
Document ID | / |
Family ID | 37884206 |
Filed Date | 2007-03-22 |
United States Patent
Application |
20070065068 |
Kind Code |
A1 |
Wang; Shih-Yuan |
March 22, 2007 |
Method and apparatus for modifying an electromagnetic radiation
beam
Abstract
Devices and methods for modifying an electromagnetic beam
include a tunable refractive medium, an input waveguide configured
for directing an incident radiation to the tunable refractive
medium, and at least one output waveguide configured for directing
a focused radiation emanating from the tunable refractive medium.
The tunable refractive medium comprises first electrodes coupled to
a first surface of a periodic dielectric medium, and second
electrodes coupled to a second surface of the periodic dielectric
medium. The periodic dielectric medium includes a dielectric
periodicity configured for providing a negative refraction of the
incident radiation and focusing the focused radiation at a focal
location. The focal location may be modified by at least one
electromagnetic signal applied between the first electrodes and the
second electrodes.
Inventors: |
Wang; Shih-Yuan; (Palo Alto,
CA) |
Correspondence
Address: |
HEWLETT PACKARD COMPANY
P O BOX 272400, 3404 E. HARMONY ROAD
INTELLECTUAL PROPERTY ADMINISTRATION
FORT COLLINS
CO
80527-2400
US
|
Family ID: |
37884206 |
Appl. No.: |
11/230159 |
Filed: |
September 19, 2005 |
Current U.S.
Class: |
385/8 ; 385/1;
385/129; 385/2; 385/31; 385/4; 385/9 |
Current CPC
Class: |
G02B 1/007 20130101;
B82Y 20/00 20130101; G02F 1/29 20130101; G02F 2202/32 20130101 |
Class at
Publication: |
385/008 ;
385/001; 385/002; 385/004; 385/009; 385/031; 385/129 |
International
Class: |
G02F 1/295 20060101
G02F001/295; G02F 1/01 20060101 G02F001/01; G02F 1/035 20060101
G02F001/035 |
Claims
1. A tunable refractive medium, comprising: a periodic dielectric
medium, comprising: an incident surface configured for receiving an
incident radiation having an incident wavelength; an emitting
surface configured for emitting a focused radiation at a wavelength
substantially near the incident wavelength; and a periodic
structure comprising a dielectric periodicity between the incident
surface and the emitting surface, the periodic structure configured
for providing a negative refraction of the incident radiation and
focusing the focused radiation at a focal location outside the
periodic dielectric medium; at least one first electrode operably
coupled to a first surface of the periodic dielectric medium; and
at least one second electrode operably coupled to a second surface
of the periodic dielectric medium; wherein the at least one first
electrode and the at least one second electrode are configured for
carrying at least one electromagnetic signal developed to modify
the focal location.
2. The device of claim 1, wherein the focused radiation at the
focal location comprises a focal area less than an area of the
incident wavelength squared.
3. The device of claim 1, wherein the focal location is modified by
at least one of a focal distance and a focal deflection from the
incident surface.
4. The device of claim 1, wherein the periodic dielectric medium
comprises a 2D photonic crystal.
5. The device of claim 4, wherein the periodic dielectric medium
comprises a first material including a plurality of periodically
spaced columns of a second material.
6. The device of claim 5, wherein the first material comprises a
dielectric material and the second material comprises air.
7. The device of claim 5, wherein the first material comprises air
and the second material comprises a dielectric material.
8. The device of claim 1, wherein the at least one electromagnetic
signal is further configured to modulate an intensity of the
focused radiation at a predetermined point in an exit medium.
9. The device of claim 1, further comprising a signal controller
configured for controlling the at least one electromagnetic signal
between the at least one first electrode and the at least one
second electrode to modify a refractive property of at least a
portion of the periodic dielectric medium to modify the focal
location.
10. An electromagnetic radiation tuning device, comprising: a
tunable refractive medium, comprising: a periodic dielectric
medium, comprising: an incident surface configured for receiving an
incident radiation having an incident wavelength; an emitting
surface configured for emitting a focused radiation at a wavelength
substantially near the incident wavelength; and a periodic
structure comprising a dielectric periodicity between the incident
surface and the emitting surface, the periodic structure configured
for providing a negative refraction of the incident radiation and
focusing the focused radiation at a focal location outside the
periodic dielectric medium; at least one first electrode operably
coupled to a first surface of the periodic dielectric medium; and
at least one second electrode operably coupled to a second surface
of the periodic dielectric medium; wherein the at least one first
electrode and the at least one second electrode are configured for
carrying at least one electromagnetic signal developed to modify
the focal location; an input waveguide configured for directing the
incident radiation to the incident surface; and at least one output
waveguide configured for directing the focused radiation.
11. The device of claim 10, wherein the focused radiation at the
focal location comprises a focal area less than an area of the
incident wavelength squared.
12. The device of claim 10, wherein the focal location is modified
by at least one of a focal distance and a focal deflection from the
incident surface.
13. The device of claim 10, wherein the periodic dielectric medium
comprises a 2D photonic crystal.
14. The device of claim 13, wherein the periodic dielectric medium
comprises a first material including a plurality of periodically
spaced columns of a second material.
15. The device of claim 14, wherein the first material comprises a
dielectric material and the second material comprises air.
16. The device of claim 14, wherein the first material comprises
air and the second material comprises a dielectric material.
17. The device of claim 10, further comprising a signal controller
configured for controlling at least one electromagnetic signal
between the at least one first electrode and the at least one
second electrode to modify a refractive property of at least a
portion of the periodic dielectric medium to modify at least one of
the focal location, the focal distance, or the focal
deflection.
18. The device of claim 17, wherein modifying the focal distance
modulates an intensity of the focused radiation incident on an
input of the at least one output waveguide.
19. The device of claim 17, wherein modifying the focal distance
modulates an intensity of the focused radiation at a predetermined
location in an exit medium.
20. The device of claim 10, wherein the at least one output
waveguide comprises a plurality of output waveguides and wherein
modifying the focal deflection directs the focal location
substantially near an input of one of the plurality of output
waveguides.
21. A method of modifying an electromagnetic radiation beam,
comprising: providing a periodic dielectric medium comprising a
negative refractive index at a wavelength of an incident radiation;
directing the incident radiation at an incident surface of the
periodic dielectric medium; generating a focused radiation at a
focal location outside the periodic dielectric medium by a negative
refraction of the incident radiation in the periodic dielectric
medium; applying at least one electromagnetic signal to at least a
portion of the periodic dielectric medium; and modifying the focal
location in response to the at least one electromagnetic
signal.
22. The method of claim 21, wherein generating the focused
radiation further comprises generating the focused radiation with
an area less than an area of the incident wavelength squared.
23. The method of claim 21, wherein the focal location is modified
by at least one of a focal distance and a focal deflection from the
incident surface of the periodic dielectric medium.
24. The method of claim 21, wherein providing the periodic
dielectric medium further comprises providing a 2D photonic crystal
comprising a first material including a plurality of periodically
spaced columns of a second material.
25. The method of claim 21, wherein applying at least one
electromagnetic signal further comprises modifying a refractive
property of at least a portion of the periodic dielectric medium to
modify at least one of the focal location, the focal distance, or
the focal deflection.
26. The method of claim 21, wherein applying at least one
electromagnetic signal further comprises modifying a refractive
property of at least a portion of the periodic dielectric medium to
modify an intensity of the focused radiation at a predetermined
point in an exit medium.
27. The method of claim 25, wherein modifying the focal distance
modulates an intensity of the focused radiation incident on an
input of at least one output waveguide.
28. The method of claim 25, wherein modifying the focal deflection
directs the focal location substantially near an input of one of a
plurality of output waveguides.
Description
FIELD OF THE INVENTION
[0001] The present invention relates generally to modifying an
electromagnetic radiation beam and more particularly to devices
with a negative refractive index and methods of focusing
electromagnetic radiation beams using negative refraction.
BACKGROUND OF THE INVENTION
[0002] Photonic crystals are a class of man-made materials, which
are often referred to as "meta-materials." Photonic crystals are
formed by dispersing a material of one dielectric constant
periodically within a matrix having a different dielectric
constant. A one-dimensional photonic crystal is a three-dimensional
structure that exhibits periodicity in dielectric constant in only
one dimension. Bragg mirrors are an example of a one-dimensional
photonic crystal. The alternating thin layers have different
dielectric constants and refractive indices. The combination of
several thin layers forms a three-dimensional structure that
exhibits periodicity in dielectric constant in only the direction
orthogonal to the planes of the thin layers. No periodicity is
exhibited in either of the two dimensions contained within the
plane of the layers.
[0003] A two-dimensional (2D) photonic crystal can be formed by
periodically dispersing rods or columns of a material of one
dielectric constant within a matrix having a different dielectric
constant. 2D photonic crystals exhibit periodicity in two
dimensions (i.e., the directions perpendicular to the length of the
rods or columns) but no periodicity is exhibited in the direction
parallel to the length of the columns.
[0004] Finally, a three-dimensional photonic crystal can be formed
by periodically dispersing small spheres or other spatially
confined areas of a first material having a first dielectric
constant within a matrix of a second material having a second,
different, dielectric constant. Three-dimensional photonic crystals
exhibit periodicity in dielectric constant in all three dimensions
within the crystal.
[0005] Photonic crystals may exhibit a photonic bandgap over a
range of frequencies in directions exhibiting periodicity in
dielectric constant. In other words, there may be a range of
frequencies of electromagnetic radiation that will not be
transmitted through the photonic crystal in the directions
exhibiting dielectric periodicity. This range of frequencies that
are not transmitted is known as a photonic bandgap of the photonic
crystal.
[0006] For an introduction to photonic crystals and their uses and
applications, the reader is referred to John D. Joannopoulos,
Robert D. Meade & Joshua N. Winn, Photonic Crystals--Molding
the Flow of Light, (Princeton University Press 1995) and K. Inoue
& K. Ithaca, Photonic Crystals--Physics, Fabrication and
Applications, (Springer 2004)
[0007] In natural materials, electromagnetic radiation is refracted
at a specific angle and in a specific direction when it encounters
a junction between two materials. A class of meta-materials has
been studied that refract electromagnetic radiation in the opposite
direction from the direction of natural materials. These materials
exhibiting negative refraction are often called super-lenses for
their ability to refract in a negative direction and, as a result,
refocus the electromagnetic radiation, rather than causing the
electromagnetic radiation to disperse. Recently, it has been shown
that photonic crystals may exhibit this negative refractive index.
Many new and useful applications may be possible for these
super-lens structures, particularly photonic crystals exhibiting
negative refraction.
BRIEF SUMMARY OF THE INVENTION
[0008] A photonic crystal exhibiting negative lens properties,
wherein the location of the focal point may be dynamically
controlled, may be valuable in a wide variety of electronic
applications.
[0009] The present invention, in a number of embodiments, includes
a tunable refractive medium and methods of modifying an
electromagnetic radiation beam. One embodiment of the present
invention includes a tunable refractive medium comprising a
periodic dielectric medium, at least one first electrode operably
coupled to a first surface of the periodic dielectric medium, and
at least one second electrode operably coupled to a second surface
of the periodic dielectric medium. The periodic dielectric medium
comprises an incident surface configured for receiving an incident
radiation having an incident wavelength, an emitting surface
configured for emitting a focused radiation at a wavelength
substantially near the incident wavelength, and a periodic
structure. The periodic structure includes a dielectric periodicity
between the incident surface and the emitting surface, wherein the
periodic structure is configured for providing a negative
refraction of the incident radiation and focusing the focused
radiation at a focal location outside the periodic dielectric
medium. In addition, the at least one first electrode and the at
least one second electrode are configured for carrying at least one
electromagnetic signal developed to modify the focal location.
[0010] Another embodiment of the present invention includes an
electromagnetic radiation tuning device, which comprises a tunable
refractive medium, an input waveguide configured for directing an
incident radiation to an incident surface of the tunable refractive
medium, and at least one output waveguide configured for directing
a focused radiation emanating from the tunable refractive medium.
The tunable refractive medium comprises a periodic dielectric
medium, at least one first electrode operably coupled to a first
surface of the periodic dielectric medium, and at least one second
electrode operably coupled to a second surface of the periodic
dielectric medium. The periodic dielectric medium comprises the
incident surface configured for receiving the incident radiation
having an incident wavelength, an emitting surface configured for
emitting the focused radiation at a wavelength substantially near
the incident wavelength, and a periodic structure. The periodic
structure includes a dielectric periodicity between the incident
surface and the emitting surface, wherein the periodic structure is
configured for providing a negative refraction of the incident
radiation and focusing the focused radiation at a focal location
outside the periodic dielectric medium. In addition, the at least
one first electrode and the at least one second electrode are
configured for carrying at least one electromagnetic signal
developed to modify the focal location.
[0011] Another embodiment of the present invention comprises a
method of modifying an electromagnetic radiation beam. The method
includes providing a periodic dielectric medium exhibiting a
negative refractive index at a wavelength of an incident radiation.
The method also includes directing the incident radiation at an
incident surface of the periodic dielectric medium. The method
further includes generating a focused radiation at a focal location
outside the periodic dielectric medium by a negative refraction of
the incident radiation in the dielectric medium. In addition, the
method includes applying at least one electromagnetic signal
through at least a portion of the periodic dielectric medium and
modifying the focal location in response to the at least one
electromagnetic signal.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0012] While the specification concludes with claims particularly
pointing out and distinctly claiming that which is regarded as the
present invention, the advantages of this invention can be more
readily ascertained from the following description of the invention
when read in conjunction with the accompanying drawings in
which:
[0013] FIG. 1A is a wave-vector diagram illustrating directions of
wave propagation at an interface between two isotropic
materials;
[0014] FIG. 1B is a wave-vector diagram illustrating directions of
wave propagation at an interface between an isotropic material and
a material exhibiting a negative refractive index;
[0015] FIG. 2 illustrates focusing properties of electromagnetic
radiation traveling through materials exhibiting a negative
refractive index;
[0016] FIG. 3A illustrates a top view of a representative periodic
dielectric medium comprising a 2D photonic crystal configured with
a triangular lattice;
[0017] FIG. 3B illustrates a top view of a representative, periodic
dielectric medium comprising a 2D photonic crystal configured with
a square lattice;
[0018] FIG. 4 is a three-dimensional view of a representative 2D
photonic crystal configured with a square lattice;
[0019] FIG. 5 is a top view of a representative electromagnetic
radiation tuning device including a 2D photonic crystal configured
with a triangular lattice;
[0020] FIG. 6 is a three dimensional view of a representative
electromagnetic radiation tuning device configured with electrodes
on a first surface and a second surface of the periodic dielectric
medium;
[0021] FIG. 7 is a top view of a representative electromagnetic
radiation tuning device coupled to a signal controller;
[0022] FIG. 8 is a top view of a representative electromagnetic
radiation tuning device illustrating dynamic focal point
tuning;
[0023] FIG. 9 is a top view of a representative electromagnetic
radiation tuning device illustrating another form of dynamic focal
point steering; and
[0024] FIG. 10 is a top view of a representative electromagnetic
radiation tuning device illustrating a de-multiplexing function
using dynamic focal point steering.
DETAILED DESCRIPTION OF THE INVENTION
[0025] In the following description, micron-scale dimensions refer
roughly to dimensions that range from one micrometer up to a few
micrometers, sub-micron scale dimensions refer roughly to
dimensions that range from 1 micrometer down to 0.05 micrometers,
and nanometer scale dimensions refer roughly to dimensions that
range from 1 nanometer up to 50 nanometers (0.05 micrometers).
[0026] The present invention, in a number of embodiments, includes
a tunable refractive medium and methods of modifying an
electromagnetic radiation beam. Embodiments of the present
invention can provide a periodic dielectric medium that includes a
negative refractive index for incident radiation having a selected
wavelength range. For incident radiation directed at an incident
surface of the periodic dielectric medium, the negative refraction
of the incident radiation that passes through the periodic
dielectric medium (PDM) and to a region beyond the periodic
dielectric medium may generate a focused radiation at a focal
location in the region beyond the PDM. Particular embodiments may
also include electrodes coupled to regions of the PDM for modifying
characteristics of the PDM. Dynamically modifying the PDM
characteristics may dynamically modify the focal location and focal
intensity of the focused radiation 330.
[0027] With regard to refraction, Snell's law is a well known law
that models refraction characteristics of a radiation beam as the
radiation beam encounters an interface between two mediums with
different refractive properties. Basically, Snell's law states that
the product of the refractive index and the sine of the angle of
incidence of a radiation beam in one medium is equal to the product
of the refractive index and the sine of the angle of refraction in
a successive medium.
[0028] Generally, naturally occurring materials exhibit a positive
refractive index. In other words, a radiation beam with an oblique
incident angle to a facet of a medium with a high positive
refractive index may be deviated toward the surface normal of the
facet. A radiation beam entering a medium of lower refractive index
may be deviated away from the surface normal, but the deviation
occurs at a positive angle relative to the surface normal.
Recently, a number of man-made materials (often referred to as
meta-materials) have been developed that exhibit a negative
refractive index. With a negative refractive index, the material
still obeys Snell's law, but the radiation beam is deviated in the
opposite direction from natural materials (i.e., with a negative
angle relative to the surface normal). Thus, using Snell's law, the
product of the refractive index and the sine of the angle of
incidence of a radiation beam in one medium is equal to the
negative of the product of the refractive index and the sine of the
angle of refraction in a successive medium.
[0029] The refractive properties of a positive refractive index and
a negative refractive index are discussed with reference to FIGS.
1A, 1B, and 2. FIG. 1A is a wave-vector diagram illustrating
directions of wave propagation through two refractive materials
(110 and 120) and at the interface between the two refractive
materials (110 and 120). Similarly, FIG. 1B is a wave-vector
diagram illustrating directions of wave propagation at an interface
between a third refractive material 130 and a negative refractive
material 140.
[0030] FIG. 1A illustrates positive refraction. In FIG. 1A the
upper circle illustrates an equal frequency surface EFS1 plot of a
first refractive material 110. The lower circle illustrates an
equal frequency surface EFS2 plot of a second refractive material
120. EFS2 is a different diameter than EFS1 due, in part, to the
difference in dielectric properties between the first refractive
material 110 and the second refractive material 120. Group velocity
vector Vg1 is oriented perpendicular to, and away from the center
of, EFS1 and illustrates the direction of wave propagation through
the first refractive material 110. A first frequency line 115
illustrates a specific frequency at which group velocity vector Vg1
intersects EFS1. The first frequency line 115 is carried down to
intersect with EFS2. Thus, a group velocity vector Vg2, oriented
perpendicular to and away from the center of EFS2, defines the
direction of wave propagation through the second refractive
material 120 at the same frequency as the wave propagating through
the first refractive material 110. The lower portion of FIG. 1A
illustrates the two group velocity vectors Vg1 and Vg2 and the
direction change that occurs at the boundary between the first
refractive medium 110 and the second refractive medium 120. The
direction change is due to the difference in the refractive index
of the two refractive materials (110 and 120). The positive
refraction can be seen by the positive angle from the surface
normal for group velocity vector Vg2.
[0031] FIG. 1B illustrates negative refraction. In FIG. 1B the
upper circle illustrates an equal frequency surface EFS3 plot of a
third refractive material 130. The lower circle illustrates an
equal frequency surface EFS4 plot of a negative refractive material
140. EFS4 is a different diameter than EFS3 due, in part, to the
difference in dielectric properties between the first refractive
material 110 and the negative refractive material 140. In addition,
in negative refractive index material 140, as the frequency
increases the equal frequency surface EFS4 moves inward around the
symmetry point. Therefore, the group velocity vector Vg4 points
inward indicating negative refraction. As a result, group velocity
vector Vg4, illustrating the direction of wave propagation through
the negative refractive material 140, is oriented perpendicular to,
but toward from the center of, EFS4.
[0032] On the other hand, the third refractive material 130 is a
positive refractive material similar to the first refractive
material 110 and the second refractive material 120. Therefore,
group velocity vector Vg3 is oriented perpendicular to and away
from the center of EFS3, and illustrates the direction of wave
propagation through the third refractive material 130. A second
frequency line 135 illustrates a specific frequency at which group
velocity vector Vg3 intersects EFS3. The second frequency line 135
is carried down to intersect with EFS4. Thus, group velocity vector
Vg4 defines the direction of wave propagation through the negative
refractive material 140 of a wave at the same frequency as the wave
propagating through the third refractive material 130. The lower
portion of FIG. 1B illustrates the two group velocity vectors Vg3
and Vg4 and the direction change that occurs at the boundary
between the third refractive medium 130 and the negative refractive
medium 140. The negative refraction can be seen by the negative
angle from the surface normal for group velocity vector Vg4.
[0033] FIG. 2 illustrates focusing properties of electromagnetic
radiation traveling through a material exhibiting a negative
refractive index. In FIG. 2, a top view illustrates a slab of
negative refractive material 140, with third refractive material
130 on opposite sides of the negative refractive material 140.
Incident electromagnetic radiation beams have first directions 132
when they impinge on a first surface 146 of the negative refractive
material 140. The negative refractive property of negative
refractive material 140 cause the electromagnetic radiation beams
to deviate towards second directions 142 with a negative angle from
the surface normal of the first surface 146. As the electromagnetic
radiation beams emit from a second surface 148 of the negative
refractive material 142, they deviate towards third directions 134.
As the electromagnetic radiation beams travel in the third
direction 134, they converge at a focal point 136.
[0034] With conventional optical focusing devices such as lenses, a
focal point is limited to near the square area of the wavelength of
the electromagnetic radiation beam squared. However, with negative
refraction, it has been shown that the focal point can be reduced
to an area significantly smaller than the wavelength squared.
[0035] Photonic crystals have been shown to posses this negative
refractive property for certain proportions of the geometry of the
photonic crystal relative to the wavelength of electromagnetic
radiation that will experience the negative refraction. Some
example embodiments of photonic crystals are shown in FIGS. 3A, 3B,
and 4.
[0036] FIG. 3A illustrates a top view of a periodic dielectric
medium 200 comprising a 2D photonic crystal 200 configured with a
triangular lattice (also referred to as a hexagonal lattice). The
2D photonic crystal 200 comprises a matrix 202 (also referred to as
a first material). Within the matrix 202, periodically spaced
columns 204 (also referred to as cylindrical regions, rods, or a
second material) are disposed in an array of horizontal rows and
vertical rows. As illustrated in FIG. 3A, these horizontal rows and
vertical rows of rods 204 may be disposed to form a triangular
lattice wherein each alternate horizontal row and vertical row is
displace about half way between the adjacent horizontal row and
vertical row.
[0037] FIG. 3B illustrates a top view of a periodic dielectric
medium 200' comprising a 2D photonic crystal 200' configured with a
square lattice, wherein the periodically spaced columns 204' in
adjacent horizontal rows and vertical rows are orthogonally
aligned. FIG. 4 shows a three-dimensional view of the 2D photonic
crystal 200' of FIG. 3A to illustrate the lengthwise dispersion of
the rods 204 through the matrix 202'.
[0038] In a 2D photonic crystal 200, the matrix 202 comprises a
first material with a first dielectric constant and the rods 204
comprise a second material with a second dielectric constant. Thus,
dielectric periodicity is exhibited in the photonic crystal in
directions perpendicular to the longitudinal axis of the rods 204.
If the difference in dielectric constant between the first material
202 and the second material 204 is large enough, a photonic bandgap
(i.e., a forbidden frequency range) may occur. This photonic
bandgap may create a variety of interesting properties for the
photonic crystal. One of those properties is negative
refraction.
[0039] By way of example and not limitation, a 2D photonic crystal
200 may comprise a matrix 202 of silicon with rods 204 of air, or a
matrix 202 of air with rods 204 of silicon. In these embodiments,
silicon has a dielectric constant of about 12 and air has a
dielectric constant of about one. Other materials, such as, for
example, InP, GaAs, and GaInAsP, have been shown to posses a
photonic bandgap in combinations with each other and with air.
Materials may be chosen to optimize a variety of parameters such as
wavelengths where the photonic bandgap occurs, ease of
manufacturing, negative refractive properties, or combinations
thereof.
[0040] Referring to FIGS. 3A and 3B, the photonic crystals have a
lattice constant 208 (a), which indicates the lateral spacing
between the centers of adjacent rods 204, and the rods 204 have a
substantially uniform radius 206 (r). For many purposes, it is
useful to discuss a relative radius (i.e. RR=r/a) or discuss the
radius 206 as a ratio of the lattice constant 208. By way of
example and not limitation, a 2D photonic crystal 200 may be
characterized with a lattice constant (a) and a radius proportional
to the lattice constant (such as, r=0.4a, and r=0.35a).
[0041] Determining the photonic band structure of a particular
photonic crystal is a complex problem that involves solving
Maxwell's equations and considering the periodic variation in the
dielectric constant through the photonic crystal. Thus, the
photonic band structure is at least partially a function of the
dielectric constant of the matrix 202, the dielectric constant of
the rods 204, the radius 206 of the rods 204, and the lattice
constant 208. Computational methods for computing the band
structure of a particular photonic crystal are known in the art. An
explanation of these computational methods may be found in John D.
Joannopoulos, Robert D. Meade & Joshua N. Winn, Photonic
Crystals--Molding the Flow of Light, (Princeton University Press
1995), in particular at Appendix D.
[0042] Simulations have shown that the negative refractive property
of a photonic crystal will be present for a range of wavelengths
(A) within a photonic bandgap of the photonic crystal. By way of
example and not limitation, Qui et al. have presented simulations
of a 2D photonic crystal 200 comprising InP-InGaAsP indicating a
refractive index of about -0.73 with a ratio of lattice constant
208 to frequency (i.e., a/.lamda.) of about 0.325 (IEEE Journal of
Selected Topics in Quantum Electronics, Vol. 9, No. 1,
January/February 2003, pp. 106-110). In other words, using this
illustrative simulation, an infrared radiation beam with a
wavelength of about 1230 nm may exhibit a refractive index of about
-0.73 when passing through the 2D photonic crystal 200 with a
lattice constant 208 of about 400 nm.
[0043] FIG. 5 is a top view of a representative electromagnetic
radiation tuning device 300 including a 2D photonic crystal 200
configured with a triangular lattice. An input waveguide 310 is
configured to guide incident radiation 320, having an incident
wavelength suitable for negative refraction, to an incident surface
210 of the 2D photonic crystal 200. As the incident radiation 320
passes through the 2D photonic crystal 200, it is refracted in a
negative direction to become refracted radiation 325 within the 2D
photonic crystal 200. As the refracted radiation 325 exits the 2D
photonic crystal 200, into an exit medium 315, it is refracted in a
negative direction again to become focused radiation 330.
[0044] The lines illustrating refracted radiation 325 and focused
radiation 330 are used to illustrate the approximate extent and
direction of the radiation beams for ideal negative refraction.
Those of ordinary skill in the art will recongnize that all
possible angles and refractions between the lines illustrating the
approximate extents are implied by the drawings illustrating
radiation beam refraction.
[0045] FIG. 5 also illustrates the focal properties possible with
negative refraction. As the incident radiation 320 enters the 2D
photonic crystal 200, the radiation beam is focused, as refracted
radiation 325, within the 2D photonic crystal 200 due to the
negative refraction at the interface between the input waveguide
310 and the 2D photonic crystal 200. The radiation beam is focused
once again, as the focused radiation 330, in the exit medium 315
due to the negative refraction between the 2D photonic crystal 200
and the exit medium 315. At a focal location 340, the focused
radiation 330 is substantially near an optimum intensity and
substantially near a minimum focal area 342. In some embodiments,
this focal area 342 may be significantly smaller than the
wavelength squared.
[0046] FIG. 6 is a three dimensional view of a representative
electromagnetic radiation tuning device 300 configured with a set
of first electrodes 360 on a first surface 230 and a set of second
electrodes 370 on a second surface 240 of the periodic dielectric
medium 200. Details of the rods 204 within the 2D photonic crystal
200 are omitted from the drawing to more clearly show the first
electrodes 360 and second electrodes 370. It is noted that the
descriptive terms first surface 230 and second surface 240 are used
for convenience of discussion rather than referring to a specific
direction or relative location. The first surface 230 and second
surface 240 may be interchangeable and refer to the surfaces in
planes substantially normal to the longitudinal axes of the rods
204 regardless of actual orientation of the 2D photonic crystal
200.
[0047] In addition, it will be recognized that the location and
arrangement of first electrodes 360 and second electrodes 370 shown
in FIG. 6 is only one representative embodiment. Many other
locations, arrangements, sizes, and geometries of the first
electrodes 360 and second electrodes 370 are contemplated within
the scope of the invention. By way of example and not limitation,
the electrodes may be round, triangular, hexagonal, or any other
suitable shapes. The arrangement may comprise more or fewer rows
and columns of electrodes on the first surface 230 and second
surface 240. The first electrodes 360 and second electrodes 370 may
be arranged in rectangular arrays, triangular arrays, hexagonal
arrays, or other configurations useful for generating negative
refractive properties.
[0048] Photonic crystals may be characterized by the permittivity
(.epsilon.) and permeability (.mu.) of the medium. Permittivity is
the dielectric property of the medium describing how an
electromagnetic field affects, and is affected by, the medium.
Permeability describes degree of magnetization of a material in
response to an electromagnetic field. While the matrix 202 and the
rods 204 may exhibit different permittivity and permeability, a
photonic crystal may be considered as having a substantially
homogenous permittivity and permeability over a general region of
the photonic crystal or over the entire photonic crystal.
[0049] For most materials, both permittivity and permeability are
generally not a constant. Rather, they may vary with the position
in the medium, the frequency of the electromagnetic field applied,
humidity, temperature, and other parameters. In addition,
permittivity and permeability may affect the refraction properties
of the photonic crystal by varying the angle of refraction.
Furthermore, the permittivity and permeability may be varied with
multiple electrodes (360 and 370) on the first surface 230 and the
second surface 240 to create localized changes in the
electromagnetic field of the 2D photonic crystal 200, localized
electrical current through the 2D photonic crystal 200, or
combination thereof. Thus, by varying the permittivity and
permeability of a 2D photonic crystal 200, the refraction angles of
the refracted radiation 325 and the focused radiation 330 may be
altered.
[0050] FIG. 7 is a top view of an electromagnetic radiation tuning
device 300 (FIG. 6) and a signal controller 400. The signal
controller 400 may generate a plurality of electromagnetic signals
390 (shown as signal busses in FIG. 7) directed to a set of
electrodes 360. In the embodiment of FIG. 7, the first electrodes
360 on the first surface 230 (FIG. 6) are shown, and for clarity,
the second electrodes 370 on the second surface 240 (FIG. 6) are
not shown. In this embodiment, the electrodes may be considered as
pairs of electrodes, one for a first electrode 360 on the first
surface 230, and one for a second electrode 370 on the second
surface 240 and opposite the first electrode 360. Thus, a pair of
electromagnetic signals 390 may be directed to each pair of
electrodes to generate an electromagnetic field therebetween, an
electrical current therebetween, or a combination thereof. As a
result, each region of the 2D photonic crystal 200 located
substantially between the electrode pair may be modified to adjust
the refractive properties of the 2D photonic crystal 200 in that
region. The signal controller 400 may control each pair of
electrodes with a different signal to generate various
electromagnetic fields at different regions of the 2D photonic
crystal 200, as explained more fully below.
[0051] FIG. 8 is a top view of an electromagnetic radiation tuning
device 300 illustrating dynamic focal point tuning. The
electromagnetic radiation tuning device 300 includes an input
waveguide 310, an exit medium 315, an output waveguide 350, and a
periodic dielectric medium 200 configured as a 2D photonic crystal
200. For ease of description, a beam axis 312 may be defined along
the longitudinal axis of the input waveguide 310 and extending
through the 2D photonic crystal 200 and the exit medium 315. For
clarity, the rods 204 of the 2D photonic crystal 200 and the second
electrodes 370 on the second surface 240 are not shown. The exit
medium 315 may be a variety of materials depending on the material
used for the 2D photonic crystal 200. By way of example and not
limitation, the exit material may be air, silicon, or Group III-IV
materials such as, InP, GaAs, and GaInAsP.
[0052] By applying electromagnetic signals 390 (not shown in FIG.
8) between various pairs of the first electrodes 360 and the second
electrodes 370, the negative refractive properties of the 2D
photonic crystal 200 may be modified. In the embodiment of FIG. 7,
the electric signals can be uniform across the entire crystal.
Thus, the refractive index of the 2D photonic crystal 200 is
modified symmetrically about the beam axis 312. However, the
symmetric modification may be modified by applying a first set of
electromagnetic signals 390 to the column of electrodes nearest the
incident surface 210 and applying a different set of
electromagnetic signals 390 to the column of electrodes near the
emitting surface 220. Thus the refractive index, while being
symmetric about the beam axis 312, may be modified at different
points along the beam axis 312.
[0053] As a result, the focused radiation 330 beam with its focal
point 340 may be modified by a focal distance along the beam axis
312 to a second focused radiation 330D2 with a second focal point
340D2. Of course, within the limits of the refractive properties of
the 2D photonic crystal 200, a focal point may be dynamically
adjusted to anywhere along the beam axis 312. This dynamic
modification of the focal point may be used for a number of
purposes. By way of example and not limitation, the focal point 340
may be modified to a position optimal for reception by the output
waveguide 350. In this way, the signal controller 400 (FIG. 7) may
modify the electromagnetic signals 390 (FIG. 7) to compensate for
variations in the permittivity and permeability of the 2D photonic
crystal 200, which may be affected by manufacturing variations,
manufacturing defects, wavelength of the incident radiation 320, or
environmental conditions.
[0054] Similarly, embodiments without an output waveguide 350 may
be used. For example, the focused radiation 330 may be used to
impinge on an analyte (not shown) located in or near the exit
medium 315. Thus, the focal point 340 may be moved to focus on the
analyte, or to focus on a variety of analytes distributed in or
near the exit medium 315 and substantially along the beam axis
312.
[0055] As another example, the electromagnetic radiation tuning
device 300 may be used as a modulator. If an output waveguide 350
is present, the focal point 340 may be moved near the output
waveguide 350 or away from the output waveguide 350, thus varying
the intensity of radiation received by the output waveguide 350. If
an output waveguide 350 is not present, by moving the focal point
340, the intensity of the focal radiation at any given point may be
modified. For example, if the focused radiation 330 is set to focus
on the focal location 340, then modified to the second focused
radiation 330D2 at the second focal location 340D2, the intensity
of radiation at the focal location 340 is reduced, thus creating a
modulation effect at the focal location 340.
[0056] FIG. 9 is a top view of an electromagnetic radiation tuning
device 300, illustrating another form of dynamic focal point
steering. In the embodiment of FIG. 9, the electromagnetic signals
390 applied to the first electrodes 360 and second electrodes 370
may be different for the electrodes on one side of the beam axis
312 relative to the electrodes on the other side of the beam axis
312. Thus, the refractive index of the 2D photonic crystal 200 may
be different on each side of the beam axis 312. Thus, the focal
point 340 may be altered by modifying the focused radiation 330
beam in the exit medium 315.
[0057] As a result, the focused radiation 330 beam with its focal
point 340 may be modified by a focal deflection substantially
perpendicular to the beam axis 312 to a third focused radiation
330D3 with a third focal point 340D3. Also illustrated is a fourth
focused radiation 330D4 with a fourth focal point 340D4. Of course,
within the limits of the refractive properties of the 2D photonic
crystal 200, a focal point 340 may be dynamically adjusted to any
location substantially perpendicular to the beam axis 312. This
dynamic modification of the focal point 340 may be used for a
number of purposes. By way of example and not limitation, the focal
point 340 may be modified to a position optimal for reception by
the output waveguide 350. In this way, the signal controller 400
may modify the electromagnetic signals 390 to compensate for
variations in the permittivity and permeability of the 2D photonic
crystal 200, which can be affected by manufacturing variations,
manufacturing defects, wavelength of the incident radiation 320, or
environmental conditions.
[0058] Similarly, embodiments without an output waveguide 350 may
be used. For example, the focused radiation 330 may be used to
impinge on an analyte (not shown) located in or near the exit
medium 315. Thus, the focal point 340 may be moved to focus on the
analyte optimally, or focus on a variety of analytes distributed
in, or near, the exit medium 315 and substantially perpendicular to
the beam axis 312.
[0059] As another example, the electromagnetic radiation tuning
device 300 may be used as a modulator, as explained above with
reference to the embodiment of FIG. 8. However, in the embodiment
of FIG. 9, the modulation occurs due to the focal point 340 being
moved by a focal deflection substantially perpendicular to the beam
axis 312.
[0060] It will be recognized that while not shown explicitly in a
drawing, the embodiments of FIG. 8 and FIG. 9 may be combined to
move the focal point 340 by both a focal distance and a focal
deflection to cover a broad area of the exit medium 315, within the
limits of the refractive properties of the 2D photonic crystal
200.
[0061] FIG. 10 is a top view of an electromagnetic radiation tuning
device 300 illustrating a de-multiplexing function using dynamic
focal point steering. In the FIG. 10 embodiment, a plurality of
output waveguides 380 are arranged at various locations aligned
with the beam axis 312, but at different offsets relative to the
beam axis 312. With this embodiment, the electromagnetic signals
390 may be modified to move the focal point 340 for optimum
placement relative to one of the output waveguides 380. In the
embodiment of FIG. 10, three output waveguides 380 are illustrated
with the focused radiation 330 and focal point 340 aligned with the
top output waveguide 380, a fifth focused radiation 330D5 with a
fifth focal point 340D5 aligned with the middle waveguide 380, and
a sixth focused radiation 330D6 with a sixth focal point 340D6
aligned with the bottom waveguide 380. Of course, within the limits
of the refractive properties of the 2D photonic crystal 200, a
focal point 340 may be dynamically adjusted to any position
substantially perpendicular to the beam axis 312, with more or
fewer output waveguides 380. Thus, by controlling the
electromagnetic signals 390, the focused radiation 330 may be
directed toward one of the waveguides forming a de-multiplexing
function.
[0062] Although this invention has been described with reference to
particular embodiments, the invention is not limited to these
described embodiments. Rather, the invention is limited only by the
appended claims, which include within their scope all equivalent
devices or methods that operate according to the principles of the
invention as described.
* * * * *